I have to give a lecture of 50 minutes with the theme "diagonalization of matrices" (basic undergrad level) for a public contest. I would like suggestions about the contents of this class. I've been thinking to give the pages 181-187 from Hoffman and Kunze's linear algebra book (maybe I will not have time to do all these pages).
What do you think is the best approach? I don't know if I start this class with eigenvalues as Hoffman and Kunze do and goes through very basic theorems about eigenvalues and diagonalizable matrices or begin with the definition of diagonalizable matrices and prove deeper theorems.